Group #18070742 — subgroups

Subgroups — #18070742

Order 4864.

630 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 630 conjugacy classes of subgroups — too many to draw. Only its 127 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#10597320	C₂	1	1	yes	maximal, characteristic
2	#14563488	C₂	1	1	yes	maximal, characteristic, complemented
3	#14561455	C₂	1	4	yes	maximal, complemented
4	C₁₉×#1839	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#10597320	C₄	1	1	yes	characteristic
6	C₂×C₄×D₇₆	—	2	1	no	—
7	C₂×C₄×D₇₆	—	2	1	no	—
8	C₂×C₄×D₇₆	C₄	1	2	yes	—
9	C₂×C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
10	C₂×#10597260	—	2	1	no	—
11	#11926446	—	2	1	no	—
12	#11926446	—	2	1	no	—
13	#11926446	C₂²	1	2	yes	—
14	#11926414	C₄	1	1	yes	characteristic
15	#11926299	C₂²	1	2	yes	—
16	C₄³×C₁₉	C₂²	1	1	yes	characteristic
17	C₁₉×#336	—	2	1	no	—
18	C₁₉×#336	—	2	1	no	—
19	C₁₉×#336	C₂²	1	2	yes	—
20	C₂²×D₇₆	—	2	1	no	—
21	C₂²×D₇₆	—	2	1	no	—
22	C₂²×D₇₆	C₂×C₄	1	2	yes	—
23	C₂²×C₄×D₁₉	—	2	2	no	—
24	C₂²×C₈×C₁₉	—	2	2	no	—
25	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
26	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
27	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
28	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
29	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
30	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
31	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
32	C₂×(C₂×D₁₉)⋊C₄	—	2	2	no	—
33	C₂×(C₂×D₁₉)⋊C₄	—	2	2	no	—
34	C₂×(C₂×D₁₉)⋊C₄	—	2	2	no	—
35	C₂×C₄⋊Dic₁₉	—	2	1	no	—
36	C₂×C₄⋊Dic₁₉	—	2	1	no	—
37	C₂×C₄⋊Dic₁₉	C₂×C₄	1	2	yes	—
38	C₂²×C₁₉⋊C₈	—	2	2	no	—
39	#10597320	—	2	4	no	—
40	C₄×D₇₆	—	4	4	no	—
41	C₄×D₇₆	—	4	2	no	—
42	C₄×D₇₆	—	4	2	no	—
43	C₄×D₇₆	—	4	4	no	—
44	C₄⋊(C₁₉⋊C₈)	—	2	4	no	—
45	#10597260	—	4	2	no	—
46	C₂³×D₁₉	—	2	2	no	—
47	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
48	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
49	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
50	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
51	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
52	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
53	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
54	C₂²×Dic₁₉	—	2	2	no	—
55	C₂×D₇₆	—	2	4	no	—
56	C₂×D₇₆	—	2	4	no	—
57	C₂×D₇₆	—	2	2	no	—
58	C₂×D₇₆	—	4	2	no	—
59	C₂×D₇₆	—	4	2	no	—
60	C₂×D₇₆	—	4	2	no	—
61	C₂×D₇₆	—	4	2	no	—
62	C₂×D₇₆	—	4	2	no	—
63	C₂×D₇₆	—	4	2	no	—
64	C₂×D₇₆	M₁₆	1	4	yes	—
65	C₂×C₄×D₁₉	—	4	4	no	—
66	C₂×C₄×D₁₉	—	4	4	no	—
67	C₂×C₄×D₁₉	—	4	4	no	—
68	C₂×C₈×C₁₉	—	4	2	no	—
69	C₂×C₈×C₁₉	—	4	2	no	—
70	C₂×C₈×C₁₉	—	4	2	no	—
71	C₄²×C₁₉	—	2	2	no	—
72	C₄²×C₁₉	—	2	2	no	—
73	C₄²×C₁₉	—	2	2	no	—
74	C₄²×C₁₉	—	2	2	no	—
75	C₄²×C₁₉	—	4	1	no	—
76	C₄²×C₁₉	—	4	1	no	—
77	C₄²×C₁₉	D₈	1	2	yes	—
78	C₄²×C₁₉	SD₁₆	1	2	yes	—
79	(C₂×D₁₉)⋊C₄	—	4	4	no	—
80	(C₂×D₁₉)⋊C₄	—	4	2	no	—
81	(C₂×D₁₉)⋊C₄	—	4	2	no	—
82	(C₂×D₁₉)⋊C₄	—	4	4	no	—
83	C₄⋊Dic₁₉	—	4	2	no	—
84	C₄⋊Dic₁₉	—	4	2	no	—
85	C₄⋊Dic₁₉	—	4	2	no	—
86	C₂×C₁₉⋊C₈	—	2	4	no	—
87	C₂×C₁₉⋊C₈	—	4	2	no	—
88	C₂×C₁₉⋊C₈	—	4	2	no	—
89	#7621	—	19	1	no	maximal, Sylow
90	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
91	C₂²×D₁₉	—	2	4	no	—
92	C₂²×D₁₉	—	4	2	no	—
93	C₂²×D₁₉	—	4	2	no	—
94	C₂²×D₁₉	—	4	2	no	—
95	C₂²×D₁₉	—	4	2	no	—
96	C₂²×D₁₉	—	4	2	no	—
97	C₂²×D₁₉	—	4	2	no	—
98	C₂×C₄×C₁₉	—	2	1	no	—
99	C₂×C₄×C₁₉	—	2	1	no	—
100	C₂×C₄×C₁₉	—	2	1	no	—
101	C₂×C₄×C₁₉	—	2	1	no	—
102	C₂×C₄×C₁₉	—	2	1	no	—
103	C₂×C₄×C₁₉	—	2	1	no	—
104	C₂×C₄×C₁₉	—	2	1	no	—
105	C₂×C₄×C₁₉	—	2	1	no	—
106	C₂×C₄×C₁₉	—	2	1	no	—
107	C₂×C₄×C₁₉	—	2	1	no	—
108	C₂×C₄×C₁₉	—	2	1	no	—
109	C₂×C₄×C₁₉	—	2	1	no	—
110	C₂×C₄×C₁₉	—	2	1	no	—
111	C₂×C₄×C₁₉	—	2	1	no	—
112	C₂×C₄×C₁₉	#100	1	2	yes	—
113	C₂×C₄×C₁₉	#102	1	2	yes	—
114	C₂×C₄×C₁₉	#102	1	2	yes	—
115	C₂×C₄×C₁₉	#104	1	2	yes	—
116	C₂×C₄×C₁₉	C₂×M₁₆	1	2	yes	—
117	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
118	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
119	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
120	C₂×Dic₁₉	—	4	2	no	—
121	C₂×Dic₁₉	—	4	2	no	—
122	C₂×Dic₁₉	—	4	2	no	—
123	D₇₆	—	4	4	no	—
124	D₇₆	—	4	4	no	—
125	D₇₆	—	4	8	no	—
126	D₇₆	—	4	8	no	—
127	C₄×D₁₉	—	8	8	no	—
128	C₈×C₁₉	—	8	2	no	—
129	C₁₉⋊C₈	—	4	4	no	—
130	C₄×#127	—	19	1	no	—
131	#1839	D₁₉	1	1	yes	characteristic, complemented
132	#1767	—	19	1	no	—
133	#1270	—	19	4	no	—
134	C₂²×C₁₉	#407	1	1	yes	characteristic
135	C₂²×C₁₉	#410	1	1	yes	characteristic
136	C₂²×C₁₉	C₂×#100	1	1	yes	characteristic
137	C₂²×C₁₉	C₂×#102	1	1	yes	characteristic
138	C₂²×C₁₉	#418	1	1	yes	characteristic
139	C₂²×C₁₉	C₂×#104	1	1	yes	characteristic
140	C₂²×C₁₉	#421	1	1	yes	characteristic
141	C₂×D₁₉	—	4	4	no	—
142	C₂×D₁₉	—	4	4	no	—
143	C₂×D₁₉	—	4	4	no	—
144	C₂×D₁₉	—	8	2	no	—
145	C₂×D₁₉	—	8	2	no	—
146	C₂×D₁₉	—	8	2	no	—
147	C₂×D₁₉	—	8	2	no	—
148	C₄×C₁₉	—	2	2	no	—
149	C₄×C₁₉	—	2	2	no	—
150	C₄×C₁₉	—	2	2	no	—
151	C₄×C₁₉	—	2	2	no	—
152	C₄×C₁₉	—	2	1	no	—
153	C₄×C₁₉	—	2	1	no	—
154	C₄×C₁₉	—	2	2	no	—
155	C₄×C₁₉	—	2	2	no	—
156	Dic₁₉	—	8	2	no	—
157	C₂×#127	—	19	1	no	—
158	C₂×C₄×D₄	—	19	2	no	—
159	C₂×C₄×D₄	—	38	1	no	—
160	C₂×C₄×D₄	—	38	1	no	—
161	C₂×C₄⋊C₈	—	38	1	no	—
162	C₂×#97	—	38	1	no	—
163	#390	—	19	2	no	—
164	#390	—	38	1	no	—
165	#390	—	38	1	no	—
166	#384	—	19	1	no	—
167	C₄³	C₂×D₁₉	1	1	yes	characteristic
168	#336	—	2	1	no	—
169	#336	—	2	1	no	—
170	#336	—	19	2	no	—
171	#336	C₂×D₁₉	1	2	yes	—
172	C₂×C₁₉	#1466	1	1	yes	characteristic
173	C₂×C₁₉	#1486	1	1	yes	characteristic
174	C₂×C₁₉	#1490	1	1	yes	characteristic
175	C₂×C₁₉	#1502	1	1	yes	characteristic
176	C₂×C₁₉	#1514	1	1	yes	characteristic
177	C₂×C₁₉	#1530	1	1	yes	characteristic
178	C₂×C₁₉	#1545	1	1	yes	characteristic
179	D₁₉	—	8	4	no	—
180	C₂²×D₄	—	19	2	no	—
181	C₂²×D₄	—	38	1	no	—
182	C₂²×D₄	—	38	1	no	—
183	C₂³×C₄	—	38	2	no	—
184	C₂²×C₈	—	2	2	no	—
185	C₂²×C₈	—	38	2	no	—
186	#127	—	38	4	no	—
187	C₄×D₄	—	76	4	no	—
188	C₄×D₄	—	76	4	no	—
189	C₄×D₄	—	76	2	no	—
190	C₄×D₄	—	76	2	no	—
191	C₂×C₄⋊C₄	—	19	2	no	—
192	C₂×C₄⋊C₄	—	38	1	no	—
193	C₂×C₄⋊C₄	—	38	1	no	—
194	C₂×C₂²⋊C₄	—	38	2	no	—
195	C₂×C₂²⋊C₄	—	38	2	no	—
196	C₂×C₂²⋊C₄	—	38	2	no	—
197	C₂×C₄²	C₄×D₁₉	1	1	yes	characteristic
198	C₂×C₄²	C₄×D₁₉	1	1	yes	characteristic
199	C₂×C₄²	D₇₆	1	1	yes	characteristic
200	C₂×C₄²	D₇₆	1	1	yes	characteristic
201	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
202	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
203	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
204	C₄⋊C₈	—	38	4	no	—
205	#97	—	76	2	no	—
206	C₁₉	#7621	1	1	yes	characteristic, complemented, Sylow
207	C₂⁴	—	38	2	no	—
208	C₂×D₄	—	19	4	no	—
209	C₂×D₄	—	38	4	no	—
210	C₂×D₄	—	38	4	no	—
211	C₂×D₄	—	38	2	no	—
212	C₂×D₄	—	76	2	no	—
213	C₂×D₄	—	76	2	no	—
214	C₂×D₄	—	76	2	no	—
215	C₂×D₄	—	76	2	no	—
216	C₂×D₄	—	76	2	no	—
217	C₂×D₄	—	76	2	no	—
218	C₂²×C₄	—	38	2	no	—
219	C₂²×C₄	—	76	4	no	—
220	C₂²×C₄	—	76	4	no	—
221	C₂²×C₄	—	76	4	no	—
222	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
223	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
224	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
225	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
226	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
227	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
228	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
229	C₂×C₈	—	4	2	no	—
230	C₂×C₈	—	4	2	no	—
231	C₂×C₈	—	4	2	no	—
232	C₂×C₈	—	38	4	no	—
233	C₂×C₈	—	76	2	no	—
234	C₂×C₈	—	76	2	no	—
235	C₄⋊C₄	—	76	2	no	—
236	C₄⋊C₄	—	76	2	no	—
237	C₄⋊C₄	—	76	2	no	—
238	C₂²⋊C₄	—	76	4	no	—
239	C₂²⋊C₄	—	76	4	no	—
240	C₂²⋊C₄	—	76	2	no	—
241	C₂²⋊C₄	—	76	2	no	—
242	C₄²	—	2	2	no	—
243	C₄²	—	2	2	no	—
244	C₄²	—	2	2	no	—
245	C₄²	—	2	2	no	—
246	C₄²	—	4	1	no	—
247	C₄²	—	4	1	no	—
248	C₄²	#64516	1	2	yes	—
249	C₄²	D₁₅₂	1	2	yes	—
250	C₂³	—	38	4	no	—
251	C₂³	—	76	2	no	—
252	C₂³	—	76	2	no	—
253	C₂³	—	76	2	no	—
254	C₂³	—	76	2	no	—
255	C₂³	—	76	2	no	—
256	C₂³	—	76	2	no	—
257	C₂³	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
258	D₄	—	76	4	no	—
259	D₄	—	76	8	no	—
260	D₄	—	76	8	no	—
261	D₄	—	76	4	no	—
262	C₂×C₄	—	2	1	no	—
263	C₂×C₄	—	2	1	no	—
264	C₂×C₄	—	2	1	no	—
265	C₂×C₄	—	2	1	no	—
266	C₂×C₄	—	2	1	no	—
267	C₂×C₄	—	2	1	no	—
268	C₂×C₄	—	2	1	no	—
269	C₂×C₄	—	2	1	no	—
270	C₂×C₄	—	2	1	no	—
271	C₂×C₄	—	2	1	no	—
272	C₂×C₄	—	2	1	no	—
273	C₂×C₄	—	2	1	no	—
274	C₂×C₄	—	2	1	no	—
275	C₂×C₄	—	2	1	no	—
276	C₂×C₄	—	76	2	no	—
277	C₂×C₄	—	76	2	no	—
278	C₂×C₄	—	76	2	no	—
279	C₂×C₄	—	152	8	no	—
280	C₂×C₄	#10597278	1	2	yes	—
281	C₂×C₄	#10597278	1	2	yes	—
282	C₂×C₄	#10597280	1	2	yes	—
283	C₂×C₄	#10597282	1	2	yes	—
284	C₂×C₄	C₂×#64516	1	1	yes	characteristic
285	C₂×C₄	C₂×D₁₅₂	1	1	yes	characteristic
286	C₂×C₄	M₁₆×D₁₉	1	2	yes	—
287	C₂×C₄	#10597395	1	2	yes	—
288	C₈	—	8	2	no	—
289	C₈	—	76	4	no	—
290	C₂²	—	76	4	no	—
291	C₂²	—	76	4	no	—
292	C₂²	—	76	4	no	—
293	C₂²	—	152	2	no	—
294	C₂²	—	152	2	no	—
295	C₂²	—	152	2	no	—
296	C₂²	—	152	2	no	—
297	C₂²	#11926507	1	1	yes	characteristic
298	C₂²	#11926517	1	1	yes	characteristic
299	C₂²	C₂×#10597280	1	1	yes	characteristic
300	C₂²	C₂×#10597278	1	1	yes	characteristic
301	C₂²	#11926548	1	1	yes	characteristic
302	C₂²	C₂×#10597282	1	1	yes	characteristic
303	C₂²	#11926562	1	1	yes	characteristic
304	C₄	—	2	2	no	—
305	C₄	—	2	2	no	—
306	C₄	—	2	1	no	—
307	C₄	—	2	1	no	—
308	C₄	—	2	2	no	—
309	C₄	—	2	2	no	—
310	C₄	—	2	2	no	—
311	C₄	—	2	2	no	—
312	C₄	—	152	2	no	—
313	C₂	—	152	4	no	—
314	C₂	#14561975	1	1	yes	characteristic
315	C₂	#14562061	1	1	yes	characteristic
316	C₂	#14562077	1	1	yes	characteristic
317	C₂	#14562131	1	1	yes	characteristic
318	C₂	#14562181	1	1	yes	characteristic
319	C₂	#14562247	1	1	yes	characteristic
320	C₂	#14562302	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₄×#10597320

C₂

yes

maximal, characteristic

#14563488

C₂

yes

maximal, characteristic, complemented

#14561455

C₂

yes

maximal, complemented

C₁₉×#1839

C₂

yes

maximal, characteristic, complemented

C₂×#10597320

C₄

yes

characteristic

C₂×C₄×D₇₆

—

C₂×C₄×D₇₆

—

C₂×C₄×D₇₆

C₄

yes

—

C₂×C₄⋊(C₁₉⋊C₈)

—

—

—

—

C₂²

yes

—

#11926414

C₄

yes

characteristic

#11926299

C₂²

yes

—

C₄³×C₁₉

C₂²

yes

characteristic

C₁₉×#336

—

C₁₉×#336

—

C₁₉×#336

C₂²

yes

—

C₂²×D₇₆

—

C₂²×D₇₆

—

C₂²×D₇₆

C₂×C₄

yes

—

C₂²×C₄×D₁₉

—

C₂²×C₈×C₁₉

—

C₂×C₄²×C₁₉

C₂×C₄

yes

characteristic

C₂×C₄²×C₁₉

C₂×C₄

yes

characteristic

C₂×C₄²×C₁₉

D₄

yes

characteristic

C₂×C₄²×C₁₉

D₄

yes

characteristic

C₂×C₄²×C₁₉

D₄

yes

characteristic

C₂×C₄²×C₁₉

D₄

yes

characteristic

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×(C₂×D₁₉)⋊C₄

—

C₂×(C₂×D₁₉)⋊C₄

—

C₂×(C₂×D₁₉)⋊C₄

—

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

C₂×C₄

yes

—

C₂²×C₁₉⋊C₈

—

#10597320

—

C₄×D₇₆

—

C₄×D₇₆

—

C₄×D₇₆

—

C₄×D₇₆

—

C₄⋊(C₁₉⋊C₈)

—

#10597260

—

C₂³×D₁₉

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×Dic₁₉

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

M₁₆

yes

—

C₂×C₄×D₁₉

—

C₂×C₄×D₁₉

—

C₂×C₄×D₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

D₈

yes

—

C₄²×C₁₉

SD₁₆

yes

—

(C₂×D₁₉)⋊C₄

—

(C₂×D₁₉)⋊C₄

—

(C₂×D₁₉)⋊C₄

—

(C₂×D₁₉)⋊C₄

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

#7621

—

maximal, Sylow

C₂³×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

100

C₂×C₄×C₁₉

—

101

C₂×C₄×C₁₉

—

102

C₂×C₄×C₁₉

—

103

C₂×C₄×C₁₉

—

104

C₂×C₄×C₁₉

—

105

C₂×C₄×C₁₉

—

106

C₂×C₄×C₁₉

—

107

C₂×C₄×C₁₉

—

108

C₂×C₄×C₁₉

—

109

C₂×C₄×C₁₉

—

110

C₂×C₄×C₁₉

—

111

C₂×C₄×C₁₉

—

112

C₂×C₄×C₁₉

#100

yes

—

113

C₂×C₄×C₁₉

#102

yes

—

114

C₂×C₄×C₁₉

#102

yes

—

115

C₂×C₄×C₁₉

#104

yes

—

116

C₂×C₄×C₁₉

C₂×M₁₆

yes

—

117

C₂×C₄×C₁₉

C₂×D₈

yes

characteristic

118

C₂×C₄×C₁₉

C₂×SD₁₆

yes

characteristic

119

C₂×C₄×C₁₉

AGL(1,ℤ/8)

yes

—

120

C₂×Dic₁₉

—

121

C₂×Dic₁₉

—

122

C₂×Dic₁₉

—

123

D₇₆

—

124

D₇₆

—

125

D₇₆

—

126

D₇₆

—

127

C₄×D₁₉

—

128

C₈×C₁₉

—

129

C₁₉⋊C₈

—

130

C₄×#127

—

131

#1839

D₁₉

yes

characteristic, complemented

132

#1767

—

133

#1270

—

134

C₂²×C₁₉

#407

yes

characteristic

135

C₂²×C₁₉

#410

yes

characteristic

136

C₂²×C₁₉

C₂×#100

yes

characteristic

137

C₂²×C₁₉

C₂×#102

yes

characteristic

138

C₂²×C₁₉

#418

yes

characteristic

139

C₂²×C₁₉

C₂×#104

yes

characteristic

140

C₂²×C₁₉

#421

yes

characteristic

141

C₂×D₁₉

—

142

C₂×D₁₉

—

143

C₂×D₁₉

—

144

C₂×D₁₉

—

145

C₂×D₁₉

—

146

C₂×D₁₉

—

147

C₂×D₁₉

—

148

C₄×C₁₉

—

149

C₄×C₁₉

—

150

C₄×C₁₉

—

151

C₄×C₁₉

—

152

C₄×C₁₉

—

153

C₄×C₁₉

—

154

C₄×C₁₉

—

155

C₄×C₁₉

—

156

Dic₁₉

—

157

C₂×#127

—

158

C₂×C₄×D₄

—

159

C₂×C₄×D₄

—

160

C₂×C₄×D₄

—

161

C₂×C₄⋊C₈

—

162

C₂×#97

—

163

#390

—

164

#390

—

165

#390

—

166

#384

—

167

C₄³

C₂×D₁₉

yes

characteristic

168

#336

—

169

#336

—

170

#336

—

171

#336

C₂×D₁₉

yes

—

172

C₂×C₁₉

#1466

yes

characteristic

173

C₂×C₁₉

#1486

yes

characteristic

174

C₂×C₁₉

#1490

yes

characteristic

175

C₂×C₁₉

#1502

yes

characteristic

176

C₂×C₁₉

#1514

yes

characteristic

177

C₂×C₁₉

#1530

yes

characteristic

178

C₂×C₁₉

#1545

yes

characteristic

179

D₁₉

—

180

C₂²×D₄

—

181

C₂²×D₄

—

182

C₂²×D₄

—

183

C₂³×C₄

—

184

C₂²×C₈

—

185

C₂²×C₈

—

186

#127

—

187

C₄×D₄

—

188

C₄×D₄

—

189

C₄×D₄

—

190

C₄×D₄

—

191

C₂×C₄⋊C₄

—

192

C₂×C₄⋊C₄

—

193

C₂×C₄⋊C₄

—

194

C₂×C₂²⋊C₄

—

195

C₂×C₂²⋊C₄

—

196

C₂×C₂²⋊C₄

—

197

C₂×C₄²

C₄×D₁₉

yes

characteristic

198

C₂×C₄²

C₄×D₁₉

yes

characteristic

199

C₂×C₄²

D₇₆

yes

characteristic

200

C₂×C₄²

D₇₆

yes

characteristic

201

C₂×C₄²

C₂²⋊D₁₉

yes

characteristic

202

C₂×C₄²

C₂²⋊D₁₉

yes

characteristic

203

C₂×C₄²

C₂²×D₁₉

yes

characteristic

204

C₄⋊C₈

—

205

#97

—

206

C₁₉

#7621

yes

characteristic, complemented, Sylow

207

C₂⁴

—

208

C₂×D₄

—

209

C₂×D₄

—

210

C₂×D₄

—

211

C₂×D₄

—

212

C₂×D₄

—

213

C₂×D₄

—

214

C₂×D₄

—

215

C₂×D₄

—

216

C₂×D₄

—

217

C₂×D₄

—

218

C₂²×C₄

—

219

C₂²×C₄

—

220

C₂²×C₄

—

221

C₂²×C₄

—

222

C₂²×C₄

(C₂×D₁₉)⋊C₄

yes

characteristic

223

C₂²×C₄

(C₂×D₁₉)⋊C₄

yes

characteristic

224

C₂²×C₄

(C₂×D₁₉)⋊C₄

yes

characteristic

225

C₂²×C₄

(C₂×D₁₉)⋊C₄

yes

characteristic

226

C₂²×C₄

C₂×C₄×D₁₉

yes

characteristic

227

C₂²×C₄

C₂×D₇₆

yes

characteristic

228

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

229

C₂×C₈

—

230

C₂×C₈

—

231

C₂×C₈

—

232

C₂×C₈

—

233

C₂×C₈

—

234

C₂×C₈

—

235

C₄⋊C₄

—

236

C₄⋊C₄

—

237

C₄⋊C₄

—

238

C₂²⋊C₄

—

239

C₂²⋊C₄

—

240

C₂²⋊C₄

—

241

C₂²⋊C₄

—

242

C₄²

—

243

C₄²

—

244

C₄²

—

245

C₄²

—

246

C₄²

—

247

C₄²

—

248

C₄²

#64516

yes

—

249

C₄²

D₁₅₂

yes

—

250

C₂³

—

251

C₂³

—

252

C₂³

—

253

C₂³

—

254

C₂³

—

255

C₂³

—

256

C₂³

—

257

C₂³

C₂×(C₂×D₁₉)⋊C₄

yes

characteristic

258

D₄

—

259

D₄

—

260

D₄

—

261

D₄

—

262

C₂×C₄

—

263

C₂×C₄

—

264

C₂×C₄

—

265

C₂×C₄

—

266

C₂×C₄

—

267

C₂×C₄

—

268

C₂×C₄

—

269

C₂×C₄

—

270

C₂×C₄

—

271

C₂×C₄

—

272

C₂×C₄

—

273

C₂×C₄

—

274

C₂×C₄

—

275

C₂×C₄

—

276

C₂×C₄

—

277

C₂×C₄

—

278

C₂×C₄

—

279

C₂×C₄

—

152

—

280

C₂×C₄

#10597278

yes

—

281

C₂×C₄

#10597278

yes

—

282

C₂×C₄

#10597280

yes

—

283

C₂×C₄

#10597282

yes

—

284

C₂×C₄

C₂×#64516

yes

characteristic

285

C₂×C₄

C₂×D₁₅₂

yes

characteristic

286

C₂×C₄

M₁₆×D₁₉

yes

—

287

C₂×C₄

#10597395

yes

—

288

C₈

—

289

C₈

—

290

C₂²

—

291

C₂²

—

292

C₂²

—

293

C₂²

—

152

—

294

C₂²

—

152

—

295

C₂²

—

152

—

296

C₂²

—

152

—

297

C₂²

#11926507

yes

characteristic

298

C₂²

#11926517

yes

characteristic

299

C₂²

C₂×#10597280

yes

characteristic

300

C₂²

C₂×#10597278

yes

characteristic

301

C₂²

#11926548

yes

characteristic

302

C₂²

C₂×#10597282

yes

characteristic

303

C₂²

#11926562

yes

characteristic

304

C₄

—

305

C₄

—

306

C₄

—

307

C₄

—

308

C₄

—

309

C₄

—

310

C₄

—

311

C₄

—

312

C₄

—

152

—

313

C₂

—

152

—

314

C₂

#14561975

yes

characteristic

315

C₂

#14562061

yes

characteristic

316

C₂

#14562077

yes

characteristic

317

C₂

#14562131

yes

characteristic

318

C₂

#14562181

yes

characteristic

319

C₂

#14562247

yes

characteristic

320

C₂

#14562302

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×(C₂×D₁₉)⋊C₄
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1839	C₂
socle	C₂³×C₁₉	C₂×C₂²⋊C₄
prime radical	C₂×#10597320	C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1839	D₁₉
hypocenter	C₁₉	#7621
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₄³ ◁ #1839

subgroup

G/H

center

C₂³

C₂×(C₂×D₁₉)⋊C₄

commutator

C₂²×C₄×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1839

C₂

socle

C₂³×C₁₉

C₂×C₂²⋊C₄

prime radical

C₂×#10597320

C₄

cosocle

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₄³ ◁ #1839

N	H ≅ G/N	type
2. #14563488	C₂	semidirect
3. #14561455	C₂	semidirect
4. C₁₉×#1839	C₂	semidirect
131. #1839	D₁₉	semidirect
206. C₁₉	#7621	semidirect

H ≅ G/N

type

2. #14563488

C₂

semidirect

3. #14561455

C₂

semidirect

4. C₁₉×#1839

C₂

semidirect

131. #1839

D₁₉

semidirect

206. C₁₉

#7621

semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₄×#10597320	2
#14563488	2
#14561455	2
C₁₉×#1839	2
#7621	19

subgroup

index

C₁₉×#1839

Subgroups — #18070742

Conjugacy classes of subgroups

Complements

Maximal subgroups